Factor the following expression: $-4$ $x^2$ $-1$ $x+$ $5$
This expression is in the form ${A}x^2 + {B}x + {C}$ . You can factor it by grouping. First, find two values, $a$ and $b$ , so: $ \begin{eqnarray} {ab} &=& {A}{C} \\ {a} + {b} &=& {B} \end{eqnarray} $ In this case: $ \begin{eqnarray} {ab} &=& {(-4)}{(5)} &=& -20 \\ {a} + {b} &=& & & {-1} \end{eqnarray} $ In order to find ${a}$ and ${b}$ , list out the factors of $-20$ and add them together. Remember, since $-20$ is negative, one of the factors must be negative. The factors that add up to ${-1}$ will be your ${a}$ and ${b}$ When ${a}$ is ${-5}$ and ${b}$ is ${4}$ $ \begin{eqnarray} {ab} &=& ({-5})({4}) &=& -20 \\ {a} + {b} &=& {-5} + {4} &=& -1 \end{eqnarray} $ Next, rewrite the expression as ${A}x^2 + {a}x + {b}x + {C}$ $ {-4}x^2 {-5}x +{4}x +{5} $ Group the terms so that there is a common factor in each group: $ ({-4}x^2 {-5}x) + ({4}x +{5}) $ Factor out the common factors: $ x(-4x - 5) - 1(-4x - 5) $ Notice how $(-4x - 5)$ has become a common factor. Factor this out to find the answer. $(-4x - 5)(x - 1)$